 Hello everyone, this is Sheela Ratnamanswade from Walshan Institute of Technology, Solapur. Today we are going to see the topic section of solids and in that particularly we will be looking into pyramids. Learning outcome. At the end of this session, students will be able to draw the sectional view of pyramid. At this moment of the video, I suggest you to pause the video and think over the structure or the shape of pyramid. As we all know, pyramids have a definite base of a triangle or a square, a polygon or some other shape. It has edges, it has faces, it has base edges, it has vertical faces, vertical edges, a common point where all these edges meet from the base at a height is called as apex. Pyramids can be a square pyramid, a hexagonal pyramid, a triangular pyramid, a pentagonal pyramid depending upon the shape of the base. Let us move further, for example, a square pyramid of side 30 mm and height 50 mm has its base on HP and two of its side of base perpendicular to VP. A section plane cuts the pyramid such that it is perpendicular to VP and inclined at 60 degrees to HP. And passes through the point on the axis 15 mm above the base of pyramid. Draw front view, sectional top view and sectional side view. Let us analyze this question. We have a square pyramid whose base side is 30 mm that is base is a square of 30 mm side. And height of axis that is the distance of apex from the base is 50 mm, this is axis height 50 mm has its base on HP that is the pyramid is resting on ground or on horizontal plane. Further, there is a condition that two of its side of base perpendicular to VP. Further, the section plane cuts the pyramid such that it passes, it is perpendicular to VP and inclined at 60 degrees to HP. When a plane is perpendicular to VP, it is seen as a line view in front view. And inclined at 60 degrees to HP, inclination with HP is seen in front view. And passes through the point on the axis 15 mm above the base of pyramid. So we have three conditions for the section plate. First condition, it is perpendicular to VP that is it will be seen as a line view in front view. The same line view is inclined at 60 degrees to HP. So the line will be inclined at 60 degrees to XY line. And the line passes through a point 15 mm above the base of the pyramid. For this condition we need to draw front view, sectional top view and sectional side view. Let us proceed with the drawing, XY line or the reference line. Now as we have seen the pyramid is resting on HP. Let us start with the top view. So in the top view we have a square of 30 mm side and we have joined the corners we are working on pyramid, the 30 mm side. Let us project these points to get the desired front view. So this is a square pyramid resting on base on HP with two of its side of base perpendicular to VP. This condition can be seen over here. So this edge, base edge and this base edge are perpendicular to VP seen in top view. This is the height and this is the naming. We have named the pyramid as base we have 1, 2, 3, 4 and apex as point. Now let us move further towards the cutting plane. So this is the cutting plane. Now wherever this cutting plane intersects with the edges of the pyramid will mark those points. The first point where it intersects is this point. Here we have two vertical edges O1 and O2 seen together in the front view. So here we obtain two points, here at the middle there is no edge and at the base we have two points one over here and one over here 15 mm above and inclined at 60 degrees. Let us project these points on the corresponding edges in the top view. So points O1 dash O2 dash will be projected on O1 and O2. Similarly the points at the base will be projected on 1, 4 and 2, 3. So let us name these points P, Q, R and S other points where the cutting plane cuts the pyramid. So when we join these points we get the required sectional top view of the pyramid cut by the given cutting plane. We dark the remaining part of the pyramid as this part has been removed it is shown in thin line. Let us move to the side view. We draw a vertical xy line, we draw the 45 degrees line. You can also draw the side view using rotation method or this 45 degrees line method. We project each and every point from the top view in the side view and from the front view. So this is the point apex point the base points we join these points. Now the cutting point wherever the cutting plane cuts O1 dash and O2 dash that point has been projected it will be on O2 and O1. So this is O, this is 1 and this is 2 and this is 1. The one point will be over here, the other point will be over here. The points on the base that is this will be at the extreme corners. So this is the required section plane sectional view of the pyramid. We will name this as P dash, Q dash, R dash and S dash. So this is the complete projection of the given square pyramid. Let us see one more example. A square pyramid of side 30 mm and height 50 mm has its base on HV with one of the edge of base parallel to VP. A section plane cuts the pyramid at an angle of 45 degrees to VP and is 6 mm away from the axis of pyramid. Draw front view, sectional top view and sectional side view. Let us begin. We have a square pyramid of base side 30 mm and height 50 mm. It is resting on HP that it has the base on HP similar to the previous example with one of the edge of base parallel to VP. We will come back to this condition. A section plane cuts the pyramid at an angle of 45 degrees to VP. The cutting plane is inclined at 45 degrees to VP. Inclination with VP is seen in top view and is 6 mm away from the axis of pyramid. Draw the front view, sectional top view and sectional side view. Let us start the drawing. The XY line now as the square pyramid is resting on HP we start with the base. We draw the base. We complete it as a pyramid by joining the opposite corners the side of 30 mm. Now we move to complete the front view. This is the front view of the pyramid. Now the condition is one of the edge of base parallel to VP. This base edge and this base edge the bottom one are parallel to XY line. So the condition is satisfied. Here we can see the same condition can be mentioned in two ways. In the previous example we have seen that two base edges are perpendicular to VP means the same condition or in the current example one of the base edge parallel to VP means the same condition. The same condition can be mentioned or put forth in two different ways. Let us move further. This is the naming naming for front view now the cutting plane. Now cutting plane is inclined at 45 degrees to VP and 6 mm away from axis. This is 45 degrees. This is the axis point O and from this we have measured 6 mm. Now the points where this cutting plane cuts the edges of the pyramid. It cuts this base edge. It cuts this vertical edge and this base edge. So we have three points one on 23, one on O3 and one on 34. Let us name these points as PQR. Let us project these points in front view. Point on 23 will be projected at the base. Here we have 2 dash, 3 dash. Similarly point Q is on vertical edge O3. O3 is represented as O3 dash in front view. So here we have that point. And point on 34 will be exactly on 3 dash, 4 dash. So these are the points. We join this. So this is the sectional view or sectional front view. We dark the remaining part. Now we move to side view 45 degrees line. We project the base. We complete the pyramid in the side view. Now the points where the cutting plane cuts the pyramid. Point Q is projected directly over here. Then we have point P projected over here. We have point Q projected over here and we have point R projected over here. So these are the points that we get in side view. Now we join these points together. So this is the sectional view in side view. We dark the remaining edges. Similarly in the top view we dark the remaining portion of the pyramid. So this is the complete projection of the pyramid when it is cut by a cutting plane inclined at 45 degrees to VP. Thank you.